This paper considers the methodology of numerical integration for prediction of dynamic response of squeeze film damper systems. A planar rotor carried in a squeeze film damper with linear centering spring is considered. Governing differential equations are expressed in polar coordinates, and fluid forces are obtained from the Ocvirk short bearing integrals. The rotating unbalance response is presented as a function of speed, unbalance, and a bearing parameter. Runge Kutta integration techniques are used to obtain numerical solutions for transient response and frequency response. The 2π film approximation results in almost linear frequency response curves. However, the π film response is very nonlinear, demonstrating the well known multiple valued response and associated hardening jump/drop phenomenon. The π film transient response is analyzed within the speed range of bistable operation to determine the effects of initial conditions, the domains of convergence, and the relative strengths of stability of each solution. The transient response is found to be most sensitive to initial values of phase angle and phase angle velocity. Initial eccentricity and eccentric velocity are much less important. In general, of the two steady state solutions, the one with lower eccentricity appears to be more stable, with a larger domain of convergence. Examples show how premature termination of the integration can lead to erroneous conclusions.

This paper considers the steady-state response due to unbalance of a planar rigid rotor carried in a short squeeze film damper with linear centering spring. The damper fluid forces are determined from the short bearing, cavitated (π film) solution of Reynold’s equation. Assuming a circular centered orbit, a change of coordinates yields equations whose steady-state response are constant eccentricity and phase angle. Focusing on this steady-state solution results in reducing the problem to solutions of two simultaneous algebraic equations. A method for finding the closed-form solution is presented. The system is nondimensionalized, yielding response in terms of an unbalance parameter, a damper parameter, and a speed parameter. Several families of eccentricity-speed curves are presented. Additionally, transmissibility and power consumption solutions are present.

A refined analytical model based on Vlasov theory is developed to (1) predict the cross-sectional stiffness constants for thin-walled multicell composite rotor blades, (2) determine the location of the shear center for thin-walled multicell composite rotor blade cross-sections, and (3) investigate the effects of using spanwise nonuniform layups to produce a desired twist distribution. The model uses an expanded Vlasov theory that includes transverse shear deformation of the cross-section, a warping function that captures the variation of shear stiffness along the contour of the cross-section, and the effect of 2D ply elasticity. Analytical results are validated with both experimental data and detailed FEM results. The effects of ignoring 2D in-plane ply elasticity, in-plane warping, and local bending moments and curvatures were investigated using the new structural model. The influence of the skin and web thickness on the shear center location and torsion rigidity was also studied. Neglecting the local shell bending moments and twists has a significant effect on torsional rigidity for relatively thicker-walled cross-sections. (Author) Abstract A refined analytical model based on Vlasov theory is developed to (1) predict the cross-sectional stiffness constants for thin walled multi-cell composite rotor blades, (2) determine the location of the shear center for thin walled multicell composite rotor blade crosssections, and (3) investigate the effects of using spanwise non-uniform lay-ups to produce a desired twist distribution. The model uses an expanded Vlasov theory that includes transverse shear deformation of the cross-section, a warping function that captures the variation of shear stiffness along the contour of the cross-section, and the effect of two-dimensional ply elasticity. Analytical results are validated with both experimental data and detailed finite element results.The effects of ignoring two dimensional inplane ply elasticity, inplane warping, and local bending moments and curvatures were investigated using the new structural model. The influence of the skin and web thickness on the shear center location and torsion rigidity was also studied. The results show that the ignoring the two-dimensional inplane ply elasticity has a significant effect on the cross-sectional stiffness. Neglecting the local shell bending moments and twists has a significant effect on torsional rigidity for relatively thicker walled cross-sections. It was found that in-plane warping is not important for thin walled closed cell cross-sections. The shear center position is ' insensitive to the airfoil skin thickness but is sensitive to the web thickness. Torsional rigidity is influenced by the airfoil skin thickness but not influenced by the web thickness for relatively thick skin airfoils. The cross-sectional model was also integrated with a structural dynamic analysis of composite rotor blades. By using spanwise uniform and non-uniform ply-layups, a preliminary investigation on the behnvior of the composite blades was conducte...

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